Once you have left the hair on the hairdresser's floor, it is no longer your property. They can do what they like with it. In your first two scenarios, you are doing nothing to modify the assumption that you have discarded the hair - you're just letting the hairdresser deal with it. In the third scenario, you are asserting that the hair is still yours; you could gather it up. Similarly, if you had left an empty soda can on a cafe table, the cafe is entitled to assume that you don't want it any longer. They could put it in the recycling bin, or make it into a delightful sculpture, or whatever. If you stop them clearing the table, and say "actually, I'd like to keep that can" - then it's still yours. If you abandon it and walk away, it's not yours.
The interpretation of whether you have "discarded" the thing is contextual. There are several possible legal theories about exactly what is going on when you leave objects lying around and wander away. These include the classical Roman view of res derelictae, that the thing becomes ownerless as soon as you physically abandon it with the intention of doing so - and conversely, views such as that of Sir Frederick Pollock, who considered it a "high, grave and dubious question" whether something stops being your property even after you throw it away while declaring that you want to get rid of it. But Pollock would allow that you had transferred ownership of the cut hair to the hairdresser, if only by silently acquiescing to them sweeping it up, rather than because they had claimed an ownerless substance. Either way, the hair is no longer your own, and once it is not yours its fate is not your concern. If you had some agreement with the hairdresser about what would happen, that's another matter, but the default position is that once the hair is theirs, they get to decide what happens with it.
The late astronaut Neil Armstrong found out his barber was selling his cut hair as souvenirs. The letter from his lawyer asks for the return of the hair, or payment of a charitable donation, on the special basis of an Ohio law protecting celebrity rights in their 'persona'. It does not assert that Armstrong had any continued property right in the hair itself. The hair samples are still for sale, by the way.
Even though your cut hair came from your body, it is not a human tissue to which special rules may apply. Hair is made of keratin and is not cellular, so nothing in the European Tissues and Cells Directive, applicable to Slovakia as an EU member, will kick in regarding your consent. Equally, this is surely not a "wrongful taking of organs, tissues [or] cells" under the Slovakian Criminal Code, sections 159-160. You may feel attached to it, in a continuing emotional sense, despite the result of the scissors: but it is not treated as specially as your actual flesh in terms of consent to what happens after it's removed.
Also in EU law, the Waste Framework Directive covers "waste", by definition, "any substance or object which the holder discards or intends or is required to discard". Although there is no coding in the European Waste Catalogue for human hair, it's classed as B3070 in the Basel Convention, an example of a B3 non-hazardous organic waste; Slovakia is one of the parties to this agreement. The substance of the Directive, as implemented in local law, would affect the onward destiny of the hair - such as which bin the hairdresser could put it in for collection, how it may be recycled into another product, or treated as a by-product instead of waste as such. There is a large and confusing case law about all that. Thankfully for you, it is the hairdresser who would have to deal with the implications.